If a mystery present is Amped when opened, it remains in your inventory as a regular, identified version. With Amped-this-level being a factor, it provides an infinite loop exploit that allows unlimited uses of key items by simply dropping all other items.

'but how would you know what is in a mystery present ahead of time? how can this be an exploit?'

Hold a present you value: rocket skates, hi tops, wings, jump 2 ship piece, etc, then when you see a Man In Black, drop all other items. Let him turn it into a mystery present, and you know its contents & can use it every level.

The abusability of this is far more straightforward than that. Get two mystery "Amp Present" presents. Get one of them amped. You now have the ability to fully amp everything in your inventory, permanently. Now find a mystery "Duplicate Present" present. You now also have the ability to duplicate every present in your inventory, permanently. No "amped-this-level" required for any of this.